Subgroups — C₁₃×#10624828 #23744979

Order 9477.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6875	C₃	1	9	yes	maximal, complemented
3	C₁₃×#6869	C₃	1	3	yes	maximal
4	C₃²×C₉×C₁₃	—	3	1	no	—
5	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
6	C₁₃×C₂₇⋊C₃	C₃²	1	9	yes	—
7	C₁₃×C₉⋊C₉	—	3	2	no	—
8	C₁₃×C₉⋊C₉	C₃²	1	3	yes	—
9	#10624828	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₃³×C₁₃	3₋¹⁺²	1	1	yes	characteristic
11	C₃×C₉×C₁₃	—	3	3	no	—
12	C₃×C₉×C₁₃	—	3	3	no	—
13	C₃×C₉×C₁₃	—	9	3	no	—
14	C₃×C₉×C₁₃	3₋¹⁺²	1	2	yes	—
15	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
16	C₁₃×C₂₇	—	3	9	no	—
17	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic
18	#6875	C₃×C₁₃	1	9	yes	complemented
19	#6869	C₃×C₁₃	1	3	yes	—
20	C₃²×C₁₃	—	3	3	no	—
21	C₃²×C₁₃	—	3	1	no	—
22	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
23	C₉×C₁₃	—	3	2	no	—
24	C₉×C₁₃	—	9	3	no	—
25	C₉×C₁₃	#737	1	3	yes	—
26	C₃²×C₉	—	3	1	no	—
27	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
28	C₂₇⋊C₃	C₃²×C₁₃	1	9	yes	—
29	C₉⋊C₉	—	3	2	no	—
30	C₉⋊C₉	C₃²×C₁₃	1	3	yes	—
31	C₃×C₁₃	—	3	1	no	—
32	C₃×C₁₃	—	3	3	no	—
33	C₃×C₁₃	#6895	1	1	yes	characteristic
34	C₃³	C₁₃×3₋¹⁺²	1	1	yes	characteristic
35	C₃×C₉	—	3	3	no	—
36	C₃×C₉	—	3	3	no	—
37	C₃×C₉	—	9	3	no	—
38	C₃×C₉	C₁₃×3₋¹⁺²	1	2	yes	—
39	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
40	C₂₇	—	3	9	no	—
41	C₁₃	#10624828	1	1	yes	characteristic, direct product factor, Sylow
42	C₃²	—	3	3	no	—
43	C₃²	—	3	1	no	—
44	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
45	C₉	—	3	2	no	—
46	C₉	—	9	3	no	—
47	C₉	C₁₃×#737	1	3	yes	—
48	C₃	—	3	1	no	—
49	C₃	—	3	3	no	—
50	C₃	C₁₃×#6895	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₃	#6895
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₁₃
prime radical	C₃³×C₁₃	3₋¹⁺²
LCS	G ▷ C₃×C₉ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₃ ◁ C₃×C₉×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₃×#6875	C₃	semidirect
9. #10624828	C₁₃	direct (N × H)
18. #6875	C₃×C₁₃	semidirect
41. C₁₃	#10624828	direct (N × H)

Subgroups — C13×#10624828 #23744979

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624828 #23744979